Efficient Decoding of Multi-Dimensional Signals From Population Spiking Activity Using a Gaussian Mixture Particle Filter

A moment-based Kalman filtering approach for estimation in ensemble systems

A persistent challenge in tasks involving large-scale dynamical systems, such as state estimation and error reduction, revolves around processing the collected measurements. Frequently, these data suffer from the curse of dimensionality, leading to increased computational demands in data processing methodologies. Recent scholarly investigations have underscored the utility of delineating collective states and dynamics via moment-based representations. These representations serve as a form of sufficient statistics for encapsulating collective characteristics, while simultaneously permitting the retrieval of individual data points. In this paper, we reshape the Kalman filter methodology, aiming its application in the moment domain of an ensemble system and developing the basis for moment ensemble noise filtering. The moment system is defined with respect to the normalized Legendre polynomials, and it is shown that its orthogonal basis structure introduces unique benefits for the application of Kalman filter for both i.i.d. and universal Gaussian disturbances. The proposed method thrives from the reduction in problem dimension, which is unbounded within the state-space representation, and can achieve significantly smaller values when converted to the truncated moment-space. Furthermore, the robustness of moment data toward outliers and localized inaccuracies is an additional positive aspect of this approach. The methodology is applied for an ensemble of harmonic oscillators and units following aircraft dynamics, with results showcasing a reduction in both cumulative absolute error and covariance with reduced calculation cost due to the realization of operations within the moment framework conceived.

Direct Discriminative Decoder Models for Analysis of High-Dimensional Dynamical Neural Data

With the accelerated development of neural recording technology over the past few decades, research in integrative neuroscience has become increasingly reliant on data analysis methods that are scalable to high-dimensional recordings and computationally tractable. Latent process models have shown promising results in estimating the dynamics of cognitive processes using individual models for each neuron's receptive field. However, scaling these models to work on high-dimensional neural recordings remains challenging. Not only is it impractical to build receptive field models for individual neurons of a large neural population, but most neural data analyses based on individual receptive field models discard the local history of neural activity, which has been shown to be critical in the accurate inference of the underlying cognitive processes. Here, we propose a novel, scalable latent process model that can directly estimate cognitive process dynamics without requiring precise receptive field models of individual neurons or brain nodes. We call this the direct discriminative decoder (DDD) model. The DDD model consists of (1) a discriminative process that characterizes the conditional distribution of the signal to be estimated, or state, as a function of both the current neural activity and its local history, and (2) a state transition model that characterizes the evolution of the state over a longer time period. While this modeling framework inherits advantages of existing latent process modeling methods, its computational cost is tractable. More important, the solution can incorporate any information from the history of neural activity at any timescale in computing the estimate of the state process. There are many choices in building the discriminative process, including deep neural networks or gaussian processes, which adds to the flexibility of the framework. We argue that these attributes of the proposed methodology, along with its applicability to different modalities of neural data, make it a powerful tool for high-dimensional neural data analysis. We also introduce an extension of these methods, called the discriminative-generative decoder (DGD). The DGD includes both discriminative and generative processes in characterizing observed data. As a result, we can combine physiological correlates like behavior with neural data to better estimate underlying cognitive processes. We illustrate the methods, including steps for inference and model identification, and demonstrate applications to multiple data analysis problems with high-dimensional neural recordings. The modeling results demonstrate the computational and modeling advantages of the DDD and DGD methods.

Enhancement of Hippocampal Spatial Decoding Using a Dynamic Q-Learning Method With a Relative Reward Using Theta Phase Precession

Hippocampal place cells and interneurons in mammals have stable place fields and theta phase precession profiles that encode spatial environmental information. Hippocampal CA1 neurons can represent the animal's location and prospective information about the goal location. Reinforcement learning (RL) algorithms such as Q-learning have been used to build the navigation models. However, the traditional Q-learning ([Formula: see text]Q-learning) limits the reward function once the animals arrive at the goal location, leading to unsatisfactory location accuracy and convergence rates. Therefore, we proposed a revised version of the Q-learning algorithm, dynamical Q-learning ([Formula: see text]Q-learning), which assigns the reward function adaptively to improve the decoding performance. Firing rate was the input of the neural network of [Formula: see text]Q-learning and was used to predict the movement direction. On the other hand, phase precession was the input of the reward function to update the weights of [Formula: see text]Q-learning. Trajectory predictions using [Formula: see text]Q- and [Formula: see text]Q-learning were compared by the root mean squared error (RMSE) between the actual and predicted rat trajectories. Using [Formula: see text]Q-learning, significantly higher prediction accuracy and faster convergence rate were obtained compared with [Formula: see text]Q-learning in all cell types. Moreover, combining place cells and interneurons with theta phase precession improved the convergence rate and prediction accuracy. The proposed [Formula: see text]Q-learning algorithm is a quick and more accurate method to perform trajectory reconstruction and prediction.

A mixed filter algorithm for sympathetic arousal tracking from skin conductance and heart rate measurements in Pavlovian fear conditioning

Pathological fear and anxiety disorders can have debilitating impacts on individual patients and society. The neural circuitry underlying fear learning and extinction has been known to play a crucial role in the development and maintenance of anxiety disorders. Pavlovian conditioning, where a subject learns an association between a biologically-relevant stimulus and a neutral cue, has been instrumental in guiding the development of therapies for treating anxiety disorders. To date, a number of physiological signal responses such as skin conductance, heart rate, electroencephalography and cerebral blood flow have been analyzed in Pavlovian fear conditioning experiments. However, physiological markers are often examined separately to gain insight into the neural processes underlying fear acquisition. We propose a method to track a single brain-related sympathetic arousal state from physiological signal features during fear conditioning. We develop a state-space formulation that probabilistically relates features from skin conductance and heart rate to the unobserved sympathetic arousal state. We use an expectation-maximization framework for state estimation and model parameter recovery. State estimation is performed via Bayesian filtering. We evaluate our model on simulated and experimental data acquired in a trace fear conditioning experiment. Results on simulated data show the ability of our proposed method to estimate an unobserved arousal state and recover model parameters. Results on experimental data are consistent with skin conductance measurements and provide good fits to heartbeats modeled as a binary point process. The ability to track arousal from skin conductance and heart rate within a state-space model is an important precursor to the development of wearable monitors that could aid in patient care. Anxiety and trauma-related disorders are often accompanied by a heightened sympathetic tone and the methods described herein could find clinical applications in remote monitoring for therapeutic purposes.